#Homework due Feb. 14, 2006

1) Consider the  set S of 100  elements
given below. It has 100 elements of the form
[[i,j],v]. Using Maple, find a polynomial in 2
variables F(x,y), of total degree 4, such that
F(i,j)=v for each [[i,j],v]

2) After you found the expression F, use xmaple
as follows:

with(plots):

implicitplot(F,x=-2..2,y=-2..2, axes=none) ;

3) printout the output

4) Cut out the shape

5) Slide it under my office door, Hill 704.


###The Set S
S:=
{[[1, 1], 7], [[5, 9], 13119], [[3, 3], 423], [[5, 8], 9320], [[1, 2], 44], [[9, 4], 10104], [[4
, 6], 3312], [[4, 7], 5119], [[4, 8], 7664], [[4, 9], 11139], [[4, 10], 15760], [[5, 1], 703], [
[5, 2], 932], [[5, 3], 1335], [[5, 4], 1984], [[5, 5], 2975], [[5, 6], 4428], [[5, 7], 6487], [[
5, 10], 18100], [[6, 1], 1407], [[6, 2], 1724], [[6, 3], 2259], [[6, 4], 3084], [[6, 5], 4295],
[[6, 6], 6012], [[6, 7], 8379], [[6, 8], 11564], [[6, 9], 15759], [[6, 10], 21180], [[7, 1], 
2551], [[7, 2], 2972], [[7, 3], 3663], [[7, 4], 4696], [[7, 5], 6167], [[7, 6], 8196], [[7, 7],
10927], [[7, 8], 14528], [[7, 9], 19191], [[7, 10], 25132], [[8, 1], 4291], [[8, 2], 4832], [[8,
3], 5703], [[8, 4], 6976], [[8, 5], 8747], [[8, 6], 11136], [[8, 7], 14287], [[8, 8], 18368], [[
8, 9], 23571], [[8, 10], 30112], [[9, 1], 6807], [[9, 2], 7484], [[9, 3], 8559], [[9, 5], 12215]
, [[9, 6], 15012], [[9, 7], 18639], [[9, 8], 23264], [[9, 9], 29079], [[9, 10], 36300], [[10, 1]
, 10303], [[10, 2], 11132], [[10, 3], 12435], [[10, 4], 14284], [[10, 5], 16775], [[10, 6], 
20028], [[10, 7], 24187], [[10, 8], 29420], [[10, 9], 35919], [[10, 10], 43900], [[4, 5], 2075],
[[1, 3], 159], [[1, 4], 424], [[1, 5], 935], [[1, 6], 1812], [[1, 7], 3199], [[1, 8], 5264], [[1
, 9], 8199], [[1, 10], 12220], [[2, 1], 31], [[2, 2], 92], [[2, 3], 243], [[2, 4], 556], [[2, 5]
, 1127], [[2, 6], 2076], [[2, 7], 3547], [[2, 8], 5708], [[2, 9], 8751], [[2, 10], 12892], [[3,
1], 111], [[3, 2], 212], [[3, 4], 816], [[3, 5], 1487], [[3, 6], 2556], [[3, 7], 4167], [[3, 8],
6488], [[3, 9], 9711], [[3, 10], 14052], [[4, 1], 307], [[4, 2], 464], [[4, 4], 1264], [[4, 3],
759]}